Almost periodic functions

Title page I. Introduction II. Purely Periodic Functiona and Their Fourier Series General Orthogonal Systems Fourier constants with respect to a normal orthogonal system. Their minimal property. Bessel's formula and Bessel's inequality Fourier series of periodic functions Operations with Fourier series Two fundamental theorems. The Uniqueness theorem and Parseval's equation Lebesgue's proof of the uniqueness theorem The multiplication theorem Summability of the Fourier series. Fejer's theorem Weierstrass' theorem Two remarks III. The theory of Almost Periodic Functions The main problem of the theory Translation numbers Definition of almost periodicity Two simple properties of almost periodic functions The invariance of almost periodicity under simple operations of calculation The mean value theorem The concept of the Fourier series of an almost periodic function. Derivation of Parseval's equation Calculations with Fourier Series The uniqueness theorem. Its equivalence with Parseval's equation The multiplication theorem Introductory remarka to the proof of the two fundamental theorems Preliminaries for the proof of the uniqueness theorem Proof of the uniqueness theorem The fundamental theorem An important example Appendix I . Generalizations of Almost Periodic Functions Appendix II . Almost Periodic Functions of a Complex Variable Bibliography